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<div class="header">
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<div class="title">HouseholderQR.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2008-2010 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2009 Benoit Jacob &lt;jacob.benoit.1@gmail.com&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// Copyright (C) 2010 Vincent Lejeune</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160; </div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#ifndef EIGEN_QR_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#define EIGEN_QR_H</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt; <span class="keyword">struct </span>traits&lt;HouseholderQR&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160; : traits&lt;MatrixType_&gt;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;{</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  <span class="keyword">typedef</span> MatrixXpr XprKind;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  <span class="keyword">typedef</span> SolverStorage StorageKind;</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;  <span class="keyword">typedef</span> <span class="keywordtype">int</span> StorageIndex;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  <span class="keyword">enum</span> { Flags = 0 };</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;};</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160; </div>
<div class="line"><a name="l00058"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html">   58</a></span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt; <span class="keyword">class </span><a class="code" href="classEigen_1_1HouseholderQR.html">HouseholderQR</a></div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SolverBase.html">SolverBase</a>&lt;HouseholderQR&lt;MatrixType_&gt; &gt;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;{</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160; </div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;    <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SolverBase.html">SolverBase&lt;HouseholderQR&gt;</a> <a class="code" href="classEigen_1_1SolverBase.html">Base</a>;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <span class="keyword">friend</span> <span class="keyword">class </span><a class="code" href="classEigen_1_1SolverBase.html">SolverBase</a>&lt;<a class="code" href="classEigen_1_1HouseholderQR.html">HouseholderQR</a>&gt;;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160; </div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    EIGEN_GENERIC_PUBLIC_INTERFACE(<a class="code" href="classEigen_1_1HouseholderQR.html">HouseholderQR</a>)</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;    };</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix</a>&lt;Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&amp;<a class="code" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a>) ? <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a> : <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a>, MaxRowsAtCompileTime, MaxRowsAtCompileTime&gt; <a class="code" href="classEigen_1_1Matrix.html">MatrixQType</a>;</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_diag_type&lt;MatrixType&gt;::type HCoeffsType;</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::plain_row_type&lt;MatrixType&gt;::type RowVectorType;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequence&lt;MatrixType,internal::remove_all_t&lt;typename HCoeffsType::ConjugateReturnType&gt;</a>&gt; <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a>;</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160; </div>
<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a8beb7206f41b0edfaef8c8acdc485743">   83</a></span>&#160;    <a class="code" href="classEigen_1_1HouseholderQR.html#a8beb7206f41b0edfaef8c8acdc485743">HouseholderQR</a>() : m_qr(), m_hCoeffs(), m_temp(), m_isInitialized(false) {}</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160; </div>
<div class="line"><a name="l00091"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a1f6d49e0344b4cf87a07a9348d31af53">   91</a></span>&#160;    <a class="code" href="classEigen_1_1HouseholderQR.html#a1f6d49e0344b4cf87a07a9348d31af53">HouseholderQR</a>(<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows, <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols)</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;      : m_qr(rows, cols),</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;        m_hCoeffs((std::min)(rows,cols)),</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;        m_temp(cols),</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;        m_isInitialized(false) {}</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160; </div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00110"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a494aa2126de8609b575f27f9b0a50c3a">  110</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1HouseholderQR.html#a494aa2126de8609b575f27f9b0a50c3a">HouseholderQR</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix)</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;      : m_qr(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;        m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;        m_temp(matrix.cols()),</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;        m_isInitialized(false)</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    {</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;      compute(matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>());</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    }</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160; </div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160; </div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00128"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a2ac3a5c49a1bd4bfe31bde5d964dbd44">  128</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1HouseholderQR.html#a2ac3a5c49a1bd4bfe31bde5d964dbd44">HouseholderQR</a>(<a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix)</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;      : m_qr(matrix.<a class="code" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>()),</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;        m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;        m_temp(matrix.cols()),</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;        m_isInitialized(false)</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    {</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;      <a class="code" href="classEigen_1_1HouseholderQR.html#a3a16530338a734971fc45efb0ef9ac94">computeInPlace</a>();</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;    }</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160; </div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="preprocessor">    #ifdef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Solve.html">Solve&lt;HouseholderQR, Rhs&gt;</a></div>
<div class="line"><a name="l00154"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a342888155081d2a5bcb22d58853a9cba">  154</a></span>&#160;    <a class="code" href="classEigen_1_1HouseholderQR.html#a342888155081d2a5bcb22d58853a9cba">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Rhs&gt;</a>&amp; b) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="preprocessor">    #endif</span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a89bc9bbb69d140898c5f5e8de11f8066">  165</a></span>&#160;    <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a> <a class="code" href="classEigen_1_1HouseholderQR.html#a89bc9bbb69d140898c5f5e8de11f8066">householderQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;HouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a>(m_qr, m_hCoeffs.conjugate());</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;    }</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160; </div>
<div class="line"><a name="l00174"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#abf306716f06675964df82b70010cf7f4">  174</a></span>&#160;    <span class="keyword">const</span> MatrixType&amp; <a class="code" href="classEigen_1_1HouseholderQR.html#abf306716f06675964df82b70010cf7f4">matrixQR</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;        eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;HouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;        <span class="keywordflow">return</span> m_qr;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;    }</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160; </div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    <a class="code" href="classEigen_1_1HouseholderQR.html">HouseholderQR</a>&amp; compute(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix) {</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;      m_qr = matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>();</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;      <a class="code" href="classEigen_1_1HouseholderQR.html#a3a16530338a734971fc45efb0ef9ac94">computeInPlace</a>();</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    }</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160; </div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1HouseholderQR.html#aaf4ef26c0b7affc91431ec59c92d64c3">absDeterminant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160; </div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;    <span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1HouseholderQR.html#af61b6dbef34fc51c825182b16dc43ca1">logAbsDeterminant</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160; </div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;    <span class="keyword">inline</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.rows(); }</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    <span class="keyword">inline</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_qr.cols(); }</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160; </div>
<div class="line"><a name="l00223"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a814dbcaa2499a0d0a6f5731001410e2d">  223</a></span>&#160;    <span class="keyword">const</span> HCoeffsType&amp; <a class="code" href="classEigen_1_1HouseholderQR.html#a814dbcaa2499a0d0a6f5731001410e2d">hCoeffs</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_hCoeffs; }</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160; </div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;<span class="preprocessor">    #ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    <span class="keywordtype">void</span> _solve_impl(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    <span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <span class="keywordtype">void</span> _solve_impl_transposed(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;<span class="preprocessor">    #endif</span></div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160; </div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160; </div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;    EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1HouseholderQR.html#a3a16530338a734971fc45efb0ef9ac94">computeInPlace</a>();</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160; </div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;    MatrixType m_qr;</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;    HCoeffsType m_hCoeffs;</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;    RowVectorType m_temp;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;};</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160; </div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00246"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#aaf4ef26c0b7affc91431ec59c92d64c3">  246</a></span>&#160;<span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1HouseholderQR.html#aaf4ef26c0b7affc91431ec59c92d64c3">HouseholderQR&lt;MatrixType&gt;::absDeterminant</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;HouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  eigen_assert(m_qr.rows() == m_qr.cols() &amp;&amp; <span class="stringliteral">&quot;You can&#39;t take the determinant of a non-square matrix!&quot;</span>);</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(m_qr.diagonal().prod());</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;}</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160; </div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00255"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#af61b6dbef34fc51c825182b16dc43ca1">  255</a></span>&#160;<span class="keyword">typename</span> MatrixType::RealScalar <a class="code" href="classEigen_1_1HouseholderQR.html#af61b6dbef34fc51c825182b16dc43ca1">HouseholderQR&lt;MatrixType&gt;::logAbsDeterminant</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;HouseholderQR is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;  eigen_assert(m_qr.rows() == m_qr.cols() &amp;&amp; <span class="stringliteral">&quot;You can&#39;t take the determinant of a non-square matrix!&quot;</span>);</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;  <span class="keywordflow">return</span> m_qr.diagonal().cwiseAbs().array().log().sum();</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;}</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160; </div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160; </div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixQR, <span class="keyword">typename</span> HCoeffs&gt;</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;<span class="keywordtype">void</span> householder_qr_inplace_unblocked(MatrixQR&amp; mat, HCoeffs&amp; hCoeffs, <span class="keyword">typename</span> MatrixQR::Scalar* tempData = 0)</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;{</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixQR::Scalar Scalar;</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixQR::RealScalar RealScalar;</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows = mat.rows();</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols = mat.cols();</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> size = (std::min)(rows,cols);</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160; </div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;  eigen_assert(hCoeffs.size() == size);</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160; </div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;Scalar,MatrixQR::ColsAtCompileTime,1&gt;</a> TempType;</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;  TempType tempVector;</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;  <span class="keywordflow">if</span>(tempData==0)</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;  {</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    tempVector.<a class="code" href="classEigen_1_1PlainObjectBase.html#a9fd0703bd7bfe89d6dc80e2ce87c312a">resize</a>(cols);</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;    tempData = tempVector.data();</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;  }</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160; </div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k &lt; size; ++k)</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;  {</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> remainingRows = rows - k;</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> remainingCols = cols - k - 1;</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160; </div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;    RealScalar beta;</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;    mat.col(k).tail(remainingRows).makeHouseholderInPlace(hCoeffs.coeffRef(k), beta);</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;    mat.coeffRef(k,k) = beta;</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160; </div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    <span class="comment">// apply H to remaining part of m_qr from the left</span></div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;    mat.bottomRightCorner(remainingRows, remainingCols)</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;        .applyHouseholderOnTheLeft(mat.col(k).tail(remainingRows-1), hCoeffs.coeffRef(k), tempData+k+1);</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  }</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;}</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160; </div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;<span class="comment">// TODO: add a corresponding public API for updating a QR factorization</span></div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;<span class="comment"></span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> MatrixQR, <span class="keyword">typename</span> HCoeffs, <span class="keyword">typename</span> VectorQR&gt;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;<span class="keywordtype">void</span> householder_qr_inplace_update(MatrixQR&amp; mat, HCoeffs&amp; hCoeffs, <span class="keyword">const</span> VectorQR&amp; newColumn,</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;                                   <span class="keyword">typename</span> MatrixQR::Index k, <span class="keyword">typename</span> MatrixQR::Scalar* tempData) {</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixQR::Index <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>;</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixQR::RealScalar RealScalar;</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;  <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows = mat.rows();</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160; </div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;  eigen_assert(k &lt; mat.cols());</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;  eigen_assert(k &lt; rows);</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  eigen_assert(hCoeffs.size() == mat.cols());</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  eigen_assert(newColumn.size() == rows);</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;  eigen_assert(tempData);</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160; </div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  <span class="comment">// Store new column in mat at column k</span></div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  mat.col(k) = newColumn;</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  <span class="comment">// Apply H = H_1...H_{k-1} on newColumn (skip if k=0)</span></div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; k; ++i) {</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> remainingRows = rows - i;</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;    mat.col(k)</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;        .tail(remainingRows)</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;        .applyHouseholderOnTheLeft(mat.col(i).tail(remainingRows - 1), hCoeffs.coeffRef(i), tempData + i + 1);</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;  }</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;  <span class="comment">// Construct Householder projector in-place in column k</span></div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;  RealScalar beta;</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;  mat.col(k).tail(rows - k).makeHouseholderInPlace(hCoeffs.coeffRef(k), beta);</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;  mat.coeffRef(k, k) = beta;</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;}</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160; </div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixQR, <span class="keyword">typename</span> HCoeffs,</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;  <span class="keyword">typename</span> MatrixQRScalar = <span class="keyword">typename</span> MatrixQR::Scalar,</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;  <span class="keywordtype">bool</span> InnerStrideIsOne = (MatrixQR::InnerStrideAtCompileTime == 1 &amp;&amp; HCoeffs::InnerStrideAtCompileTime == 1)&gt;</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;<span class="keyword">struct</span> householder_qr_inplace_blocked</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;{</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;  <span class="comment">// This is specialized for LAPACK-supported Scalar types in HouseholderQR_LAPACKE.h</span></div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">void</span> run(MatrixQR&amp; mat, HCoeffs&amp; hCoeffs, <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> maxBlockSize=32,</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;      <span class="keyword">typename</span> MatrixQR::Scalar* tempData = 0)</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;  {</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixQR::Scalar Scalar;</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;    <span class="keyword">typedef</span> Block&lt;MatrixQR,Dynamic,Dynamic&gt; BlockType;</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160; </div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows = mat.rows();</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols = mat.cols();</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> size = (std::min)(rows, cols);</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160; </div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;    <span class="keyword">typedef</span> Matrix&lt;Scalar,Dynamic,1,ColMajor,MatrixQR::MaxColsAtCompileTime,1&gt; TempType;</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;    TempType tempVector;</div>
<div class="line"><a name="l00355"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a9a9377aab1cea26db5f25bab7e682f8f">  355</a></span>&#160;    <span class="keywordflow">if</span>(tempData==0)</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;    {</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;      tempVector.resize(cols);</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;      tempData = tempVector.data();</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;    }</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160; </div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> blockSize = (std::min)(maxBlockSize,size);</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160; </div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0;</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    <span class="keywordflow">for</span> (k = 0; k &lt; size; k += blockSize)</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    {</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> bs = (std::min)(size-k,blockSize);  <span class="comment">// actual size of the block</span></div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> tcols = cols - k - bs;              <span class="comment">// trailing columns</span></div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> brows = rows-k;                     <span class="comment">// rows of the block</span></div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160; </div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;      <span class="comment">// partition the matrix:</span></div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;      <span class="comment">//        A00 | A01 | A02</span></div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;      <span class="comment">// mat  = A10 | A11 | A12</span></div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;      <span class="comment">//        A20 | A21 | A22</span></div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;      <span class="comment">// and performs the qr dec of [A11^T A12^T]^T</span></div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;      <span class="comment">// and update [A21^T A22^T]^T using level 3 operations.</span></div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;      <span class="comment">// Finally, the algorithm continue on A22</span></div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160; </div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;      BlockType A11_21 = mat.block(k,k,brows,bs);</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;      <a class="code" href="classEigen_1_1Block.html">Block&lt;HCoeffs,Dynamic,1&gt;</a> hCoeffsSegment = hCoeffs.segment(k,bs);</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160; </div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;      householder_qr_inplace_unblocked(A11_21, hCoeffsSegment, tempData);</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160; </div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;      <span class="keywordflow">if</span>(tcols)</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;      {</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;        BlockType A21_22 = mat.block(k,k+bs,brows,tcols);</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;        apply_block_householder_on_the_left(A21_22,A11_21,hCoeffsSegment, <span class="keyword">false</span>); <span class="comment">// false == backward</span></div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;      }</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    }</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;  }</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;};</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160; </div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160; </div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;<span class="preprocessor">#ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;<span class="keywordtype">void</span> HouseholderQR&lt;MatrixType_&gt;::_solve_impl(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rank = (std::min)(rows(), cols());</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160; </div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;  <span class="keyword">typename</span> RhsType::PlainObject c(rhs);</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160; </div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;  c.applyOnTheLeft(householderQ().setLength(rank).adjoint() );</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160; </div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;  m_qr.topLeftCorner(rank, rank)</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;      .template triangularView&lt;Upper&gt;()</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;      .solveInPlace(c.topRows(rank));</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160; </div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;  dst.topRows(rank) = c.topRows(rank);</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;  dst.bottomRows(cols()-rank).setZero();</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;}</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160; </div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt;</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;<span class="keywordtype">void</span> HouseholderQR&lt;MatrixType_&gt;::_solve_impl_transposed(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rank = (std::min)(rows(), cols());</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160; </div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;  <span class="keyword">typename</span> RhsType::PlainObject c(rhs);</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160; </div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;  m_qr.topLeftCorner(rank, rank)</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;      .template triangularView&lt;Upper&gt;()</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;      .transpose().template conjugateIf&lt;Conjugate&gt;()</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;      .solveInPlace(c.topRows(rank));</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160; </div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;  dst.topRows(rank) = c.topRows(rank);</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;  dst.bottomRows(rows()-rank).setZero();</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160; </div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;  dst.applyOnTheLeft(householderQ().setLength(rank).<span class="keyword">template</span> conjugateIf&lt;!Conjugate&gt;() );</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;}</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160; </div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00440"></a><span class="lineno"><a class="line" href="classEigen_1_1HouseholderQR.html#a3a16530338a734971fc45efb0ef9ac94">  440</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1HouseholderQR.html#a3a16530338a734971fc45efb0ef9ac94">HouseholderQR&lt;MatrixType&gt;::computeInPlace</a>()</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;{</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;  <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> rows = m_qr.rows();</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;  <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols = m_qr.cols();</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;  <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> size = (std::min)(rows,cols);</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160; </div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;  m_hCoeffs.resize(size);</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160; </div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;  m_temp.resize(cols);</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160; </div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;  internal::householder_qr_inplace_blocked&lt;MatrixType, HCoeffsType&gt;::run(m_qr, m_hCoeffs, 48, m_temp.data());</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160; </div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;}</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160; </div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;<span class="keyword">const</span> <a class="code" href="classEigen_1_1HouseholderQR.html">HouseholderQR&lt;typename MatrixBase&lt;Derived&gt;::PlainObject</a>&gt;</div>
<div class="line"><a name="l00461"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a9a9377aab1cea26db5f25bab7e682f8f">  461</a></span>&#160;<a class="code" href="classEigen_1_1MatrixBase.html#a9a9377aab1cea26db5f25bab7e682f8f">MatrixBase&lt;Derived&gt;::householderQr</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1HouseholderQR.html">HouseholderQR&lt;PlainObject&gt;</a>(eval());</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;}</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160; </div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160; </div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_QR_H</span></div>
<div class="ttc" id="aclassEigen_1_1Block_html"><div class="ttname"><a href="classEigen_1_1Block.html">Eigen::Block</a></div><div class="ttdoc">Expression of a fixed-size or dynamic-size block.</div><div class="ttdef"><b>Definition:</b> Block.h:107</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html">Eigen::HouseholderQR</a></div><div class="ttdoc">Householder QR decomposition of a matrix.</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:60</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_a1f6d49e0344b4cf87a07a9348d31af53"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a1f6d49e0344b4cf87a07a9348d31af53">Eigen::HouseholderQR::HouseholderQR</a></div><div class="ttdeci">HouseholderQR(Index rows, Index cols)</div><div class="ttdoc">Default Constructor with memory preallocation.</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:91</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_a2ac3a5c49a1bd4bfe31bde5d964dbd44"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a2ac3a5c49a1bd4bfe31bde5d964dbd44">Eigen::HouseholderQR::HouseholderQR</a></div><div class="ttdeci">HouseholderQR(EigenBase&lt; InputType &gt; &amp;matrix)</div><div class="ttdoc">Constructs a QR factorization from a given matrix.</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:128</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_a342888155081d2a5bcb22d58853a9cba"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a342888155081d2a5bcb22d58853a9cba">Eigen::HouseholderQR::solve</a></div><div class="ttdeci">const Solve&lt; HouseholderQR, Rhs &gt; solve(const MatrixBase&lt; Rhs &gt; &amp;b) const</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_a3a16530338a734971fc45efb0ef9ac94"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a3a16530338a734971fc45efb0ef9ac94">Eigen::HouseholderQR::computeInPlace</a></div><div class="ttdeci">void computeInPlace()</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:440</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_a494aa2126de8609b575f27f9b0a50c3a"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a494aa2126de8609b575f27f9b0a50c3a">Eigen::HouseholderQR::HouseholderQR</a></div><div class="ttdeci">HouseholderQR(const EigenBase&lt; InputType &gt; &amp;matrix)</div><div class="ttdoc">Constructs a QR factorization from a given matrix.</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:110</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_a814dbcaa2499a0d0a6f5731001410e2d"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a814dbcaa2499a0d0a6f5731001410e2d">Eigen::HouseholderQR::hCoeffs</a></div><div class="ttdeci">const HCoeffsType &amp; hCoeffs() const</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:223</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_a89bc9bbb69d140898c5f5e8de11f8066"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a89bc9bbb69d140898c5f5e8de11f8066">Eigen::HouseholderQR::householderQ</a></div><div class="ttdeci">HouseholderSequenceType householderQ() const</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:165</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_a8beb7206f41b0edfaef8c8acdc485743"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#a8beb7206f41b0edfaef8c8acdc485743">Eigen::HouseholderQR::HouseholderQR</a></div><div class="ttdeci">HouseholderQR()</div><div class="ttdoc">Default Constructor.</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:83</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_aaf4ef26c0b7affc91431ec59c92d64c3"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#aaf4ef26c0b7affc91431ec59c92d64c3">Eigen::HouseholderQR::absDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar absDeterminant() const</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:246</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_abf306716f06675964df82b70010cf7f4"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#abf306716f06675964df82b70010cf7f4">Eigen::HouseholderQR::matrixQR</a></div><div class="ttdeci">const MatrixType &amp; matrixQR() const</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:174</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderQR_html_af61b6dbef34fc51c825182b16dc43ca1"><div class="ttname"><a href="classEigen_1_1HouseholderQR.html#af61b6dbef34fc51c825182b16dc43ca1">Eigen::HouseholderQR::logAbsDeterminant</a></div><div class="ttdeci">MatrixType::RealScalar logAbsDeterminant() const</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:255</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderSequence_html"><div class="ttname"><a href="classEigen_1_1HouseholderSequence.html">Eigen::HouseholderSequence</a></div><div class="ttdoc">Sequence of Householder reflections acting on subspaces with decreasing size.</div><div class="ttdef"><b>Definition:</b> HouseholderSequence.h:123</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition:</b> MatrixBase.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a9a9377aab1cea26db5f25bab7e682f8f"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a9a9377aab1cea26db5f25bab7e682f8f">Eigen::MatrixBase::householderQr</a></div><div class="ttdeci">const HouseholderQR&lt; PlainObject &gt; householderQr() const</div><div class="ttdef"><b>Definition:</b> HouseholderQR.h:461</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors.</div><div class="ttdef"><b>Definition:</b> Matrix.h:182</div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_a9fd0703bd7bfe89d6dc80e2ce87c312a"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#a9fd0703bd7bfe89d6dc80e2ce87c312a">Eigen::PlainObjectBase::resize</a></div><div class="ttdeci">void resize(Index rows, Index cols)</div><div class="ttdef"><b>Definition:</b> PlainObjectBase.h:283</div></div>
<div class="ttc" id="aclassEigen_1_1Solve_html"><div class="ttname"><a href="classEigen_1_1Solve.html">Eigen::Solve</a></div><div class="ttdoc">Pseudo expression representing a solving operation.</div><div class="ttdef"><b>Definition:</b> Solve.h:65</div></div>
<div class="ttc" id="aclassEigen_1_1SolverBase_html"><div class="ttname"><a href="classEigen_1_1SolverBase.html">Eigen::SolverBase</a></div><div class="ttdoc">A base class for matrix decomposition and solvers.</div><div class="ttdef"><b>Definition:</b> SolverBase.h:71</div></div>
<div class="ttc" id="aclassEigen_1_1SolverBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::SolverBase&lt; HouseholderQR&lt; MatrixType_ &gt; &gt;::derived</a></div><div class="ttdeci">HouseholderQR&lt; MatrixType_ &gt; &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62"><div class="ttname"><a href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">Eigen::ColMajor</a></div><div class="ttdeci">@ ColMajor</div><div class="ttdef"><b>Definition:</b> Constants.h:321</div></div>
<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f"><div class="ttname"><a href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">Eigen::RowMajor</a></div><div class="ttdeci">@ RowMajor</div><div class="ttdef"><b>Definition:</b> Constants.h:323</div></div>
<div class="ttc" id="agroup__flags_html_gae4f56c2a60bbe4bd2e44c5b19cbe8762"><div class="ttname"><a href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">Eigen::RowMajorBit</a></div><div class="ttdeci">const unsigned int RowMajorBit</div><div class="ttdef"><b>Definition:</b> Constants.h:68</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition:</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a554f30542cc2316add4b1ea0a492ff02"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Eigen::EigenBase::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdoc">The interface type of indices.</div><div class="ttdef"><b>Definition:</b> EigenBase.h:41</div></div>
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